Linked Questions
25 questions linked to/from Why shouldn't the denominator of the covariance estimator be n-2 rather than n-1?
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Why absolute value of eigenvalues are used in PCA or LDA?
In PCA and LDA techniques, eigenvectors with the $k$ largest eigenvalues give principal components. However, when selecting these eigenvalues, are they to be sorted by the absolute value (regardless ...
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How is $\text{Cov}(\bar{Y}, Y_i - \bar{Y}) = \dfrac{1}{n^2} \text{Cov} \left( \sum_{j = 1}^n Y_j, nY_i - \sum_{j = 1}^n Y_j \right)$?
I have this example of sufficiency:
Let $Y_1, \dots, Y_n$ be i.i.d. $N(\mu, \sigma^2)$. Note that $\sum_{i = 1}^n (y_i - \mu)^2 = \sum_{i = 1}^n (y_i - \bar{y})^2 + n(\bar{y} - \mu)^2$. Hence
$$\...
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Rationale for elliptical region of correlations in gene expression data
I am analysing an RNA seq data set and I am trying to look at correlation between expression values of significant genes in 4 different biological duplicates and their clinical parameters.
Here, I ...
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Law of total covariance with two conditioning variables
How to decompose the covariance with two conditioning random variables?
For example, there is a law of total variance with two conditioning variables in the Wikipedia
$$
\text{Var}(Y)=\text{E}[\text{...
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how to find asymptotic joint distribution of two linear combination of order statistics?
Suppose I have n order statistics from some unknown continuous distribution funciton F(x), $X_{1}\leqslant X_{2}\leqslant...\leqslant X_{n}$. And I have two linear combination of these order ...
- 290
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Unbiased estimator variance of sample variance
I was reading the section on k-statistics on wolfram alpha. It was known to me that for the sample variance
$k_2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2$
it holds that its variance ...
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Is the covariance between the product of two variables and one of the variables zero?
For two centered (zero expectation) random variables $X$ and $Z$ I am interested in the covariance of the product $XZ$ and either $X$ or $Z$.
$$Cov(X,XZ) = E( X(XZ - E(XZ))) = E(X^2Z)$$
I think the ...
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Distribution of the average of multivariate normals?
I have seen that the sum of $n$ iid multivariate normal vectors (mean $\mu$ and variance $\Sigma$), $X_1+\dots+X_n$, is distributed as a normal with mean $n\mu$ and variance $n\Sigma$. Is the ...
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The covariance of a data matrix
Please let me know if the below statement is valid or not ;
Suppose that $X$ is an $n\times p$ data matrix with $p$ features and $n$ data samples.
Suppose further that each feature(column) is zero ...
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Calculate multivariate betas using correlations and standard deviations [duplicate]
In a simple regression context:
$$
y = \alpha + \beta x + e
$$
We can estimate beta from:
$$
\hat{\beta} = \frac{cov(x,y)}{var(x)} = \rho_{xy} \frac{\sigma_y}{\sigma_x}
$$
This last decomposition is ...
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